(CBS News) "Nothing good" will come if Congress fails to raise the debt ceiling, Treasury Secretary Jack Lew warned Sunday on "Face the Nation," calling on House Speaker John Boehner, R-Ohio, to "give the majority a chance to vote."

As the United States heads into its second week of a partial government shutdown, Congress now heads toward an Oct. 17 deadline to avoid a first-ever default on its financial obligations. Lew argued the heart of the problem isn't "the president's willingness to negotiate," as Boehner has suggested - "the problem is we have not yet engaged with Republicans who are willing to put everything on the table."

Boehner has reiterated time and again that his chamber doesn't have the votes for the Democrat-proposed "clean" bill, without strings attached like provisions to alter or delay "Obamacare."

"Well then why doesn't he put it on the floor and give it a chance?" Lew asked Sunday. "There's a majority in Congress that I believe is prepared to do the right thing, to open the government and make sure we don't cross over that abyss."

"Congress needs to do its job; it needs to open the government up and it needs to make it possible for us to pay our bills on time," Lew said. "Let's remember how we got here: Over the summer a bunch of fairly extreme members of the Republican Party said, 'We're going to use shutting down the government or defaulting our debt as a way to go back and re-argue the Affordable Care Act.' That was a bad decision."

Lew cautioned Republicans against issuing threats: "What we've seen is these demands, 'Unless I get my way, you know, that we'll bring these terrible consequences of shutdown or default.'"

But it's President Obama, Senate Minority Whip John Cornyn, R-Texas, argued later on the program, who's been "AWOL" in budget negotiations.

"The president's got to lead and he's got to do his job," he said. "We rejected the concept of a king, when our country was founded, and created three co-equal branches of government. The president said he won't negotiate on the continuing resolution and now he said he won't negotiate on the debt. But what he needs to do is roll up his sleeves and get to the table and I'm sure we can get past the impasse on both the continuing resolution, as well as the debt ceiling."

Cornyn suggested the administration remains wary from the near-government shutdown in 2011.

"The president now realizes that Republicans, who were concerned about spending levels, got the better of him on the Budget Control Act, which has actually cut $2 trillion over the next ten years," he said. "And the president realizes that he's going to have to give something in order to get what he wants, and he doesn't want to go there."